Two Families of Linear Codes Containing Non-GRS MDS Codes
This provides new code constructions for coding theory, but appears incremental as it modifies existing GRS codes.
The paper constructs two new families of linear codes by modifying GRS code generator matrices, deriving parity-check matrices and conditions for MDS property, and identifies non-GRS MDS subfamilies with self-orthogonal/dual characterizations.
We construct two new families of linear codes by modifying the generator matrices of generalized Reed-Solomon (GRS) codes. For these codes, we explicitly derive parity-check matrices and establish necessary and sufficient conditions ensuring the MDS property. Additionally, we explore subfamilies within these constructions that are non-GRS MDS codes. We also characterize their self-orthogonal and self-dual properties and present some explicit constructions and examples.